Note: This started as a reply to a comment of an earlier post ; since one can’t easily add formatting, pictures etc. in a comment, i decided to publish it in form of a post.
Nicolas (1739-1792) and his brother Robert (1754-1854) Delaunay (sometimes also referred to as De Launay) were both active as engravers/etchers in Paris. Nicolas, pupil of Louis-Simon Lempereur (1728-1808) and later entitled to Graveur du Roi (“Royal Engraver” of Louix XV), was one of the contributors of engravings to the 1773-83 edition of J. J. Rousseau’s Oeuvre Complètes (Complete Works) after designs of Jean Michel Moreau (also called Moreau le Jeune).
One of Nicolas Delaunays most popular compositions after Jean-Honoré Fragonard (1732-1806) is Les hasards heureux de l’escarpolette (“The Happy Accidents of a Child’s Swing“). Artheque cites also La bonne mère as one of his “big” compositions.
Jean-Honoré Fragonard painted several versions of La Bonne Mère (“The good mother“). Emma Barker parker puts the painting in a “genre galant” context, combining “eroticism and domesticity in a distinctly comic fashion” . The young woman, supposedly to watch over the two small children, seems distracted by the white cat and the boy pouring water to her right. She does not exhibit the complete absorption in her maternal duties expressed in scenes by Chardin for example. The title La bonne mère is not by Fragonard, this is a later addition by the engraver Nicolas Delaunay. The title was subsequently also used for the painting, emphasizing the domestic component of the composition.
The print La bonne mère by is a combined etching and engraving, Delaunay created it in 1779 , during the same time he had published a series of engravings/etchings depicting domestic scenes and maternal duties. This series included five mirrored prints after compositions by Fragonard (including L’Heureuse fécondité, Dites-donc, s’il-vous-plait, Les baignets ) and Le Bonheur du ménage, after Jean-Baptiste Le Prince (1734-1781)  .
La bonne mère is dedicated to the fermier-général , Ménage de Pressigny (“dédiée à Monsieur de Pressigny Conseiller Fermier Generale de sa Majesté”), who had owned the painting (“Tire du Cabinet de M: Menage de Pressigny”), shown above, now in a private collection. It appears together with the mentioned Les hasards heuereux de l’escarpolette on a price list issued by the engraver . Both prints were a huge success already at that time. In the case of La bonne mère, the prints seemed almost to surpass the popularity of the painting, or at least the watercolor drawing by Fragonard of the same scene, (exhibited in 1781), which was praised as depicting “a topic, well known by the nice engraving by M. de Launay” .
 Emma Barker, Greuze and the Painting of Sentiment, 2005, p. 120.
 Emma Barker, Greuze and the Painting of Sentiment, 2005, p. 272, note 23.
 Jean Siméon Chardin 1699-1779: Werk, Herkunft, Wirkung, 1999, p. 415.
 Emma Barker, Greuze and the Painting of Sentiment, 2005, p. 133.
 Emma Barker, Greuze and the Painting of Sentiment, 2005, p. 274, note 54.